The success of a business project often relies on the accuracy of its schedule. Inaccurate and overoptimistic schedules can lead to significant project failures. In this paper, we explore whether the presence of anchors, such as relatively uninformed suggestions or expectations of the duration of project tasks, play a role in the project estimating and planning process. Our laboratory experiment contributes to the methodology of investigating the robustness and persistence of the anchoring effect in the following ways: (1) we investigate the anchoring effect by comparing the behavior in low and high anchor treatments with a control treatment where no anchor is present; (2) we provide a more accurate measurement by incentivizing participants to provide their best duration estimates; (3) we test the persistence of the anchoring effect over a longer horizon; (4) we evaluate the anchoring effect also on retrospective estimates. We find strong anchoring effects and systematic estimation biases that do not vanish even after the task is repeatedly estimated and executed. In addition, we find that such persisting biases can be caused not only by externally provided anchors, but also by the planner's own initial estimate